Elephants, Donkeys, and Colonel Blotto
Ivan P. Yamshchikov and Sharwin Rezagholi
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
Electoral Competition, Classification of Political Issues, Dynamic Stochastic Blotto Game, Adaptive Learning.
This paper employs a novel method for the empirical analysis of political discourse and develops a model that
demonstrates dynamics comparable with the empirical data. Applying a set of binary text classifiers based
on convolutional neural networks, we label statements in the political programs of the Democratic and the
Republican Party in the United States
. Extending the framework of the Colonel Blotto game by a stochastic
activation structure, we show that, under a simple learning rule, the simulated game exhibits dynamics that
resemble the empirical data.
The donkey is a symbol of the Democratic Party and the elephant is a symbol of the Republicans.
Electoral competition, the attempt of political actors
to unite a large fraction of the voting population be-
hind them, is of utmost importance in democratic sys-
tems. In this note we gather preliminary empirical
insight into how political organizations divide their
activities among political issues. We use data from
political manifestos of English-speaking countries to
classify the contents of US political manifestos into
issues. We visualize the time-path of the fraction
of statements dedicated to certain issues within the
political programs. We use these empirical results
to motivate a game-theoretic toy model of a biparti-
san democracy, which we explore numerically. This
model, under certain conditions, demonstrates behav-
ior similar to the manifesto data. The numerical re-
sults suggest that this capability is due to our intro-
duction of a stochastic activation structure of political
issues in the voting population.
In the spirit of complex systems, we conceptual-
ize political parties as adaptive agents in an uncertain
environment, where they use a form of local optimiza-
tion, while the outcome of their behavior depends on
the opposing parties.
We first present our empirical results, then our toy
model and its numerical analysis, and finally subsume
and sketch possible future lines of research.
This project has received funding from the European
Union’s Horizon 2020 research and innovation programme
under grant agreement No 732942.
It is not easy to measure the dynamics of political de-
bates, although the Internet, with its wealth of data,
has made it easier to measure some aspects of polit-
ical discussions, see, for example, (Jungherr, 2014),
(Neuman et al., 2014) or (Graham et al., 2016). For a
detailed discussion of the connection between politi-
cal discussions, and the language used in them, we ad-
dress the reader to the monographs of (Chilton, 2004)
and (Parker, 2014). For a discussion of opinion polar-
ization we point to (Banisch and Olbrich, 2017). In
this note we try to obtain an intuition on the dynamics
of the political debate by looking at the programs of
political parties.
Programs of political parties are well-documented
in developed countries. In this paper we focus on
party programs from the United Kingdom, Canada,
and the United States, which are collected in the Man-
ifesto database (Lehmann et al., 2017). We only work
with programs in the English language. The applica-
tion of the proposed methods to other countries and
languages is within the scope of future research. The
Manifesto corpus consists of documents of different
types. Some of them are annotated texts, where each
(semi-) sentence is classified into one, and only one,
category, others are plain texts, or scanned copies.
There are seven categories in the Manifesto corpus:
We retain the categories of the dataset, but give them
names that we hope are more precisely interpretable.
Yamshchikov, I. and Rezagholi, S.
Elephants, Donkeys, and Colonel Blotto.
DOI: 10.5220/0006761601130119
In Proceedings of the 3rd International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2018), pages 113-119
ISBN: 978-989-758-297-4
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
Foreign policy issues, with subcategories such as
internationalism, foreign special relationships, or
military issues.
Freedom and law issues, with subcategories such
as human rights, democracy, or constitutionalism.
Government issues, with subcategories such as
centralization, administrative efficiency, or polit-
ical corruption.
Economic policy issues, with subcategories such
as technology, infrastructure, growth, or eco-
nomic regulation.
Social policy issues, with subcategories such as
equality, welfare state, or education.
Cultural policy issues, with subcategories such as
national way of life, traditional morality, or mul-
Target groups issues, with subcategories such as
appeal to labor groups, farmers, middle class, or
The categories listed above can be highly fragmented,
but we believe that this level of generality is still suit-
able to analyze the macro-dynamics of political dis-
The annotated data for the UK is available from
1997 to 2015, for the US the annotated data is avail-
able from 2004 to 2012, for Canada from 2011 to
2015. The time span for each country is extremely
small, covers only a limited number of elections, and
does not allow to see the long-term dynamics of polit-
ical debate. The plain-text data from the US goes as
far back as 1960. We are especially interested in the
US, since we hypothesize that the dynamics of a bi-
partisan system are comparatively simple. One needs
to come up with a way to classify the non-annotated
texts. One needs a classifier that associates each sen-
tence in the non-annotated program to a category from
the list above. Convolutional neural networks are a ro-
bust tool for tasks of this sort. Following the approach
proposed by (Kim, 2014) we train seven binary classi-
fiers on the annotated programs from the UK, the US,
and Canada and apply these classifiers to the histor-
ical programs of the Democratic and the Republican
Party of the United States. Details on the obtained
classifiers are given in the Appendix.
Figure 1 shows the dynamics of seven categories
in the political programs of Democrats and Republi-
cans. Each subfigure shows the percentage of text in
the program addressing a specific issue. These esti-
mates are imperfect (the accuracy of each classifier is
around 70% on the test data), but since we apply the
same classifiers to Republican and Democratic pro-
grams and Figure 1 depicts the percentage of sen-
tences out of the total number of classified sentences,
the visualization captures the qualitative dynamics of
the discourse. Indeed Figure 1 provides several inter-
esting insights.
There are patterns which can be attributed to the
actual history of the political process: In the eight-
ies Democrats start to constantly pay more atten-
tion to social issues; In 2000 there is a rapid in-
crease in Republican attention to culture-related is-
sues. Other interesting patterns are surges of attention
to government-related issues in the Republican pro-
grams of 1964 (after the death of Kennedy) and 1976
(after Watergate). It is interesting that the parties stay
relatively close to each other on each issue. This is
surprising, since we are talking about the percentage
of the program devoted to a certain topic. If we look
closely at presidential election results, we see another
interesting pattern. If we give one point to the pres-
idential candidate whose party has devoted a larger
fraction of their program to a given issue, and give
zero points to the candidate whose party devoted a
smaller percentage to the issue, we see that, in the ma-
jority of the cases, the scores would be 4:3 or 3:4. In
most cases the candidate whose score exceeds the op-
ponent’s wins the election. The scores are not always
close to each other: Richard Nixon and Bill Clinton
win their first elections with 5:2 in 1972 and 1992 re-
spectively. Ronald Reagan is reelected in 1984 with
5:2, on the verge of 6:1.
These empirical results suggest the following ex-
planation. As long as political parties compete across
a number of different issues, the amount of resources
that each party allocates to a given issue is propor-
tional to its success among the voters that pay at-
tention to the issue. The success of one party in a
category can be modeled as ’the winner takes it all’:
The party that allocated more resources to the issue
’wins’ it, while the opposing party ’looses’ the issue.
The party that ’gets the most issues’ wins the elec-
tion. Models with this structure are known in political
science and economics as Colonel Blotto games. In
the following sections we propose the extension of a
Blotto game to model the dynamics of political dis-
course, run a simulation of this model, and briefly dis-
cuss its qualitative behavior.
Mathematical social scientists have used a game-
theoretical model, originally conceived by (Borel,
1921) and typically referred to as the Colonel Blotto
game, to model electoral competition. In the origi-
nal setup of the game the military commander Blotto
is tasked to divide his troops among a finite number
COMPLEXIS 2018 - 3rd International Conference on Complexity, Future Information Systems and Risk
Figure 1: Political discourse in the US, triangles mark wins of party candidates in presidential elections.
of battlefields while his opponent does the same with
his troops. A battlefield is won by the commander
whose troops are in the majority on the respective bat-
tlefield. The commander who wins most of the battle-
fields wins the game.
While the Blotto game has been of interest to com-
binatorially inclined game theorists, it also became
popular as a model of electoral competition (Myer-
son, 1993). A thorough mathematical treatment of
the game and a characterization of its equilibria is
given by (Roberson, 2006a). For an analysis of re-
distributional politics on the basis of a Blotto model
see (Laslier and Picard, 2002), who also provide an
extensive bibliography. The equilibria of generalized
Elephants, Donkeys, and Colonel Blotto
versions of the classic Blotto game are studied by
(Kovenock and Roberson, 2015). A one-shot model
with uncertainty that is similar to our setup is consid-
ered by (Osorio, 2013).
We study a continuous Blotto game (Gross and
Wagner, 1950), where two players, henceforth called
political parties, are endowed with a continuously di-
visible resource that they allocate between a finite
number of battlefields, henceforth called political is-
sues. One interpretation of the resource is as the me-
dia budget of the respective parties, which can be used
to disseminate information, or even propaganda, on
certain issues. Another interpretation of the resource
is as the effort that politicians, or candidates for of-
fice, spend on furthering certain issues. Henceforth
we will refer to the resource as the budget. We further
allow asymmetry in the budgets, a stochastic activa-
tion structure of political issues (coupled with a lim-
ited form of history dependence), and consider polit-
ical parties that use a myopic adaption rule. To our
knowledge a comparable model has not yet been con-
Consider two political parties, indexed by i
{1, 2}. The parties are endowed with budgets, mod-
eled as real intervals [0, b
], b
> 0. The parties al-
locate their budgets to a finite set of political issues
{1, ..., n}. The game proceeds in stages, indexed by
t N
. At t = 0 the game is initialized with some
initial allocation of resources b
(0), where σ
({1, ..., n}) and (A) denotes the probability sim-
plex over the finite set A. Party 1 wins the election in
round t if
(t) b
> 0. (1)
The winning condition for party 2 is symmetric.
Should the equation hold as an equality the election is
drawn. The above equation encodes that party 1 wins
the election in period t if it has allocated its resources
such that the weighted sum of allocation differences
is in its favor. The weighting vector (w
(t), ..., w
in equation (1) is determined according to
(t) =
1 with p
0 with 1 p
and is initialized as
(0) =
1 with probability p
0 with probability 1 p
where the vector (p
, ..., p
) (0, 1)
parametrizes in-
dependent Bernoulli distributions. A more realistic
model would incorporate a correlation structure be-
tween the activation of issues. This extension is a path
for further research. The weighting vector consists of
entries from {0, 1} which are redrawn independently
in every period with a history dependent adjustment
parametrized by m N. The Bernoulli probability of
activation of an issue is adjusted downwards accord-
ing to the length of its activation period. In partic-
ular, if an issue has been activated for m periods its
activation probability vanishes entirely. This is meant
to introduce some change of the political landscape:
An issue cannot be important forever. Even if an is-
sue is important with high probability (the p
eter is close to one), it will sometimes be deactivated.
Therefore changes of the political landscape provide
a chance to parties with a small budget: Although the
party with the higher budget can heavily cater to high-
probability issues, the party with smaller budget can
invest in a special interest’ that might be sporadically
activated. Our way of setting up the game is basically
the plurality version of the Blotto game (Laslier and
Picard, 2002) with the addition of the weighting term.
We equip the parties with adaptive rules for action
adjustment that can be described by the following pro-
cedure for each party
Calculate new policy
(t +1) = σ
(t) + s
(t) σ
(t))w(t), (4)
where σ
(t) is the policy of the opponent on the
previous step.
Check that the new policy is positive σ
(t +1) > 0.
Shift policies uniformly so that each σ
(t + 1) is
non negative
Normalize σ
(t + 1) so that it satisfies the budget
(t +1) = 1
The parameter s
(0, 1) is the speed of adjustment.
This is an imitation-heuristic. The actions are ini-
tialized randomly. The adjustment rule is myopic in
the sense that parties do not explicitly reason about
the reaction of the political opponent and enact lo-
cal, instead of global, optimization. We believe that
this admits a fairly natural interpretation. Political or-
ganizations comprise many decentralized individual
actors and organizations, political action groups, lob-
byists, special interest groups, long-term media rela-
tions, and so on. We suggest the interpretation of the
adjustment rule as the outcome of mass action.
While an analytical treatment of this type of model
is of interest, we will now present preliminary numer-
ical results in the next section.
COMPLEXIS 2018 - 3rd International Conference on Complexity, Future Information Systems and Risk
We perform a number of simulations according to the
strategy described in Equation 3. We demonstrate
that, despite its simplicity, our approach shows inter-
esting results. The results of the simulation can be
related to the empirical data described in Section 2.
The number of issues is set to equal 7, the number of
issues in the empirical data in Section 2.
Before we discuss the results of our simulations,
let us briefly elaborate on the parameters of the model.
Since the importance of an issue in an election de-
pends on a probability p
, which can differ across is-
sues, it makes sense to explore at least three different
regimes of issue activation:
All issues are activated fairly often,
All issues are activated rarely,
Some issues are activated much more often than
the others.
The parameter m in Equation 2 can be interpreted as
the ’inertia’ of the voters’ opinions: They still pay at-
tention to issues that are in fact already obsolete. The
speed of the adjustments s
controls how fast parties
can reallocate their resources from an issue to another.
The model allows every party to have a different bud-
get b
. These budgets are parameters corresponding
to the collective efforts of the party to dominate in
the political discussion. We assume the budgets to be
equal in our simulations, however further exploration
of the model without this constraint is of interest, es-
pecially in a multi-party setup. Figure 2 shows a sim-
ulation of 20 rounds of the game where some issues
are activated much more often than the others. The
triangles are denoting the winner of the election, as
in the empirical results shown in Figure 1. The path
dependence is relatively small (m = 3) and the speed
of adjustment is relatively high (s
= s
= 0.1). One
can see how the red player adjusts her stance on issue
6 on the 11th round and captures issues 1, 2 and 7.
As time passes the system approaches an equilib-
rium. Convergence is faster if parties can reallocate
their resources quicker or if issues are activated more
often. Rare feature-activation increases the fuzziness
of the process. Generally, there are two distinct modes
of the system: The first could be called competitive
democracy, the second one-party-dominance with ex-
ogenous shocks. The competitive regime is charac-
terized by political parties that are ’responsive’ to the
challenges (higher speeds of the players) and ’prob-
lems’ that occur relatively rarely (issues get activated
rarely, only a few are present at every given time).
In this mode leadership moves from one party to the
other often, as newly activated issues are captured by
one of the parties. One can see the typical dynam-
ics of one issue under these conditions in Figure 3.
The leadership changes several times and the winner
keeps the position for longer periods of time.
The system enters the other regime if the problems
are persistent (the p
-values are relatively close to 1)
and political parties are not very ’flexible’ (s
and s
are small). In this mode one party captures the lead-
ership due to a strong initial position and loses it only
for short periods of time, due to the exogenous issue-
deactivation, rather than due to the actions of the op-
ponent. The parties are not flexible and can not aptly
respond to the challenges that they face. The opposi-
tion can capture power for a short period of time due
to exogenous shock but the ’usual’ political order is
soon restored. In Figure 4 one can see the dynamics
of an issue in this regime. Since most of the issues
are active most of the time and the speed s
of the par-
ties is low, the parties have little chance to reallocate
resources in a way that would allow them to win and
keep winning for some time. Changes of leadership
occur due to exogenous shocks and the power goes
back to the dominant player (the blue one in Figure 4)
after a short period of time.
This note is a foray that could be taken further and in-
vestigated in greater detail. First, using data from the
Manifesto project database (Lehmann et al., 2017),
we have trained 7 binary classifiers based on a pre-
trained convolutional neural network built according
to (Kim, 2014). The obtained classifiers have demon-
strated relatively high precision on the test data (pre-
cision was around 70%) and allowed us to label his-
torical political programs of Democrats and Republi-
cans going as far back as 1960. Second, an analysis
of the labeled historical data supports the hypothesis
that the dynamics of political discourse follow a form
of the Colonel Blotto game. This opinion was previ-
ously voiced in relation to different aspects of the po-
litical process ((Washburn, 2013), (Roberson, 2006b),
(Kovenock and Roberson, 2015)) but this is, to our
knowledge, the first paper where this hypothesis is
complemented by empirical data. Third, a dynamic
stochastic model of electoral competition with learn-
ing and history dependence is provided. It is an exten-
sion of the Colonel Blotto game that we also believe
to be novel. The extension of the model to multiple
parties, and the empirical justification of such an ex-
tension by data from a multi-party electoral system,
are a matter for future research. Finally, a simulation
Elephants, Donkeys, and Colonel Blotto
Figure 2: Simulation of political discourse across 7 issues and 20 elections, triangles mark wins of party candidates.
with a simple policy update-rule is able to produce
data that shares the qualitative properties of the em-
pirical findings. Models of the type presented here
may be developed further to provide insights into, at
least the qualitative, phenomena in electoral competi-
tion. The ultimate aim of social science is of course
prediction, but we do not believe that this is a realistic
target. Still, providing tractable models of electoral
competition might allow us to develop deeper insight
into possible futures and to identify the key mecha-
nisms of political change.
COMPLEXIS 2018 - 3rd International Conference on Complexity, Future Information Systems and Risk
Figure 3: Red player captures and holds the third issue on
the 12th round but it does not secure her position fully.
Figure 4: Blue player’s domination fails due to random
shocks rather than to issue capture.
The authors are grateful to Eckehard Olbrich and
Sven Banisch for fruitful and interesting discussions
and their advice and support.
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In (Kim, 2014) it is shown that, despite little tun-
ing of hyperparameters, a simple neural network with
one layer of convolution performs remarkably well on
sentence-classification tasks, when provided with un-
supervised pre-training of word vectors. We followed
the proposed method and built seven binary classi-
fiers where we used labeled sentences from (Lehmann
et al., 2017) as positive examples and randomly se-
lected sentences with different label from the same
data set as negative ones. The accuracy results of the
vanilla classifiers on test data are provided in Table 1.
Table 1: Obtained binary classifiers.
Category Size of train Test accuracy
Foreign policy 8486 69.3
Freedom and law 4442 70.1
Government 9554 70.5
Economic policy 22013 71.4
Social policy 26340 72.1
Cultural policy 9136 69.8
Target groups 9256 69.3
Elephants, Donkeys, and Colonel Blotto